CFO Estimation with ICI Cancellation for OFDM Systems

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CFO Estimation with ICI Cancellation for OFDM Systems

吳宗威

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Outline

Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

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Outline


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Motivations

Motivations

Every OFDM model has a specific form in the carrier frequency offset system.

When we estimate the frequency offset by pilot,the ICI still exists. It is intuitive to decrease the ICI first , then estimate it.

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Outline


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OFDM System Model

C is pilot sequence h is time domain channel impulse response w is additive white Gaussian noise. N data information {S(k)} which have been modulated with N modulation

values {X(k)} on every sub-carrier

x ( t )

Channel h ( t)

S ( k)

r (t )ˆ ( )S k

S/P

P/S

X (k ) x ( n)

Adding Pilots C(n) &IFFT

AddingCyclicPrefix & P/S

DACSignal

Mapper

z (t )

( )R k

FFT RemoveCyclicPrefix & S/P

ADC

SignalDemapper

( )r n

AWGN w ( t)

The OFDM system model:

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OFDM System Model

The nth sample of an OFDM block generated by IFFT :

N: number of subcarriersNg: length of cyclic prefix

12 /

0

1( ) ( ) ,0 1

Nj kn N

k

x n X k e n NN

[ ( ),..., ( 1), (0),..., ( 1)]gx x N N x N x x N

z x h

( ) ( ) ( )r n z n w n

12 /

0

( ) ( ) ,0 1N

j kn N

n

R k r n e k N

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UWB Channel Model

Four environments in this UWB channel model: CM1 model is based on LOS (0-4m) channel

measurements in [2]

Time

Signal strength

: cluster decay factor : path decay factor : cluster arrival rate : the arrival rate of path within each cluster

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Outline


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Sensitivity for Carrier Frequency Offset

The OFDM system model with CFO:

x ( t )

Channel h ( t)

S ( k )

S/P

X ( k ) x(n)

Adding Pilots C(n)& IFFT

AddingCyclicPrefix & P/S

DACSignal

Mapper

z (t )

r (t )ˆ ( )S k

P/S

( )R k

FFTRemoveCyclicPrefix & S/P

ADC

SignalDemapper

( )r n

AWGN w ( t)

02 /fj n Ne

is the ratio of the actual frquency offset to the sub-carrier spacing/f f f

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The n-th received sample of the m-th symbol is given by

FFT 12 /

0

1 12 ( ) / 2 /2 / 2 /

0 0

1 12 ( ) / 2 ( ) /

0 0

( ) ( ) ,0 1

1 ( )

( )

1 ( )

g g f f

g g f f

Nj kn N

m mn

N Nj mN mN N N j n Nj kn N j in N

m ii n

m

N Nj mN mN N N j n i k N

m ii n

R k r n e k N

e X i H e e eN

W k

e X i H eN

( )mW k

( ) ( ) ( ) ( )m mm mR k S k I k W k

2 ( ) /( ) ( ) (n),0 1f g gj mN mN N n Nm m mr n z n e w n N

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Amplitude reduction: Phase shift:


2 ( ) / ( 1) /

m

sin( )S ( ) ( ) ( )

sin( )f g g f

f

j mN mN N N j N Nfm m

N

k X k H k e eN

sin( )

sin( )f

f

NN

2( ) ( 1) /f g gmN mN N N N

.

.1

( )( 1) / 2 ( ) /

( )0,

sin( ( ))( ) ( ( ) ( ))

sin( )f f g g

f

Nj i k N N j mN mN N Nf

m mm i ki i k N

i kI k X i H i e e

N

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Pilot tone - aided CFO Estimation

PTA with weighting (PTAW) CFO estimation:

* *2 arg ( ) ( ) ( ) ( ) ,gf PTAW m m D m m D i

n P

N ND R n R n C n C n n P

N

* *1 1arg ( ) ( ) ( ) ( )

2f PTAW m m D m m Dn Pg

NR n R n C n C n

N N D

f

Let P denote the set of indexes of the Np pilot carriers

I

QR1 R2

Pilot1 (n1)

Pilot2 (n2)

Pilot3 (n3)

t

Rm Rm+D

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Outline


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Matrix form of R(k)

2 ( ) /( ) ( ) (n),0 1f g gj mN mN N n Nm m mr n z n e w n N

12 /

0

( ) ( ) ( ).N

j in N

m m mi

n i i eZ X H

( ) ( )* ( )z n x n h n

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2 ( ( ) 0) /

2 ( ( ) 1) /

.0

0

j f m N Ng Ng N

j f m N Ng Ng N N

r ze

e

2 ( ( ) 0) /

2 ( ( ) 1) /

1

0

1

1

(0) (0)

( 1)( 1)

0

0

0

0

0

0

j f m N Ng Ng N

j f m N Ng Ng N N

N

H X

F

X NH N

F H X

e

e

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R F r

12 /

0

( ) ( ) ,0 1N

j kn Nm m

n

R k r n e k N

0

1

1

0

0N

F F H X

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A math property

A(k) , k=0…N-1 is the DFT of

a(n) , n=0,…,N-1

(0) (1) ( 1)

(0)

( 1) (0) ( 2)1

( 1)(1) ( 1) (0)

0

0

N

N N

NN

F F

a a aA

a a a

A a a a

0

1

1

0 1 1

1 0 2

1 2 1 0

0

0N

N

N N

N N

R F F H X

H X

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The Problem

Can we find a matrix B, such that

0 1 1

1

1 0 2

1 2 1 0

( )

B

( )

0

0

N

N N

N

N N

f

f

1

1

( ) (0) (0)

.

( 1) ( 1)( )

( ) (0) (0)

=

( ) ( 1) ( 1)

0

0 N

N

f H X

B R

H N X Nf

f H X

f H N X N

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B is in fact a matrix that does Gaussian

Reduction to

0 1 1

1 0 2

1 2 1 0

N

N N

N N

( )exp( 2 ( ) ) /

nj m f N Ng Ng n N

( ) ( )( )

k nifft

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The term is the key point .Because if the ratio between each term is irrelevant to , then we can definitely finish the matrix B.

sin( ( ))

sin( ( ) / )

f k

f k N

( )exp( 2 ( ) / ) exp( ( 1) / )

kj m f N Ng Ng N j f N N

sin( ( ))exp( ( 1) / )

sin( ( ) / )

f kj k N N

f k N

f

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The numerator of is actually .

And the denominator because

So, we can regard as

Thus, the ratio between each term is irrelevant to .

sin( ( ))f k sin( )f

/f N 0sin( / )k N

( )k

f

sin( )exp( ( 1) / )

sin( / )

fj k N N

k N

sin( ( ))

sin( ( ) / )

f k

f k N

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However, is zero when k=0 . So we need a estimate for the denominator of

Choose the PTAW estimate for the denominator of

B is the matrix does Gaussian reduction to the cyclic matrix

composed of

sin( / )k N

f̂ (0)

(0)

( )

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sin( / )

( 1)exp( ( 1) / ) 1,...... 1

sin( / )

k k

kf N

j k N N k Nk N

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The Procedure

Step1: Estimate the frequency offset by PTAW

Step2: Substitute the estimate into the denominator of

Step3: multiply the matrix B with the incoming symbol and the previous symbol

Step4: Apply the PTAW again, then we have a more accurate estimate.

(0)

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Outline


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Different Modulation

0 5 10 15 20 25 30 35 40 45 5010

-6

10-5

10-4

10-3

10-2

SNR(dB)

MS

E

N=128 Np=12 DF=0.1

BPSK-PTAW

BPSK-PTAW-mine

BPSK

270 5 10 15 20 25 30 35 40 45 5010

-6

10-5

10-4

10-3

10-2

SNR(dB)

MS

E

N=128 Np=12 DF=0.1

QPSK-PTAW

QPSK-PTAW-mine

QPSK

280 5 10 15 20 25 30 35 40 45 5010

-6

10-5

10-4

10-3

10-2

SNR(dB)

MS

E

N=128 Np=12 DF=0.1

8PSK-PTAW

8PSK-PTAW-mine

8PSK

290 5 10 15 20 25 30 35 40 45 5010

-6

10-5

10-4

10-3

10-2

SNR(dB)

MS

E

N=128 Np=12 DF=0.1

16PSK-PTAW

16PSK-PTAW-mine

16PSK

300 5 10 15 20 25 30 35 40 45 5010

-6

10-5

10-4

10-3

10-2

SNR(dB)

MS

E

N=128 Np=12 DF=0.1

BPSK-PTAW

BPSK-PTAW-mine

QPSK-PTAWQPSK-PTAW-mine

8PSK-PTAW

8PSK-PTAW-mine

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Recursive

Recursive

0 5 10 15 20 25 30 35 40 45 5010

-6

10-5

10-4

10-3

10-2

SNR(dB)

MS

E

N=128 Np=12 DF=0.1

16PSK-PTAW

16PSK-PTAW-1st

16PSK-PTAW-2nd16PSK-PTAW-3rd

16PSK-PTAW-True

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Random initial condition

0 5 10 15 20 25 30 35 40 45 5010

-6

10-5

10-4

10-3

10-2

SNR(dB)

MS

E

N=128 Np=12 DF=0.1

16PSK-PTAW

16PSK-PTAW-seed1

16PSK-PTAW-seed216PSK-PTAW--seed3

16PSK-PTAW-True

Random initial condition =0.5 Delta_f=0.1

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Outline


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Conclusions

Advantages: The key advantages of our proposed algorithms is to p

rovide more accurate frequency synchronization . Estimate the frequency offset without knowing the ch

annel response first.

Complexity: N*Np multiplier .

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Thank you ~

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Reference

[1] J. R. Foerster, Ed., “Channel Modeling Sub-committee Report Final,” IEEE P802.15 SG3a contribution.

[2] H. Chen and G.J. Pottie, "A Comparison of Frequency Offset Tracking Algorithms for OFDM", GLOBECOM '03, vol.2, pp. 1069-1073, Dec. 2003.

[3] K. Shi, E. Serpedin, and P. Ciblat, “Decision-directed fine synchronization for coded OFDM systems,” in Proc. IEEE International Conf. on Acoustics, Speech, and Signal Processing. (ICASSP’04), vol. 4, pp. 365-368, 17-21 May 2004.

CFO Estimation with ICI Cancellation for OFDM Systems

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